The solution to the given system of equations is (x, y). What is the value of y?x = 4y =...

1. TRANSLATE the problem information

• Given system:
  • \(\mathrm{x = 4}\) (first equation gives x directly)
  • \(\mathrm{y = 5 - x}\) (second equation expresses y in terms of x)

• What we need to find: The value of y

2. INFER the solution strategy

• Since the first equation directly tells us \(\mathrm{x = 4}\), we can substitute this value into the second equation
• This substitution method will give us the value of y

3. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{x = 4}\) into the second equation:
  \(\mathrm{y = 5 - x}\)
  \(\mathrm{y = 5 - 4}\)
  \(\mathrm{y = 1}\)

Answer: A. 1

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students correctly solve the system but answer with the value of x instead of y.

They calculate \(\mathrm{x = 4}\) and \(\mathrm{y = 1}\) correctly, but when they see "What is the value of y?", they accidentally select the x-value they found. Since they remember working with \(\mathrm{x = 4}\) prominently in their solution, they may select Choice B (4).

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors during substitution.

When calculating \(\mathrm{y = 5 - 4}\), they might accidentally add instead of subtract (\(\mathrm{y = 5 + 4 = 9}\)) or make other computational mistakes. This could lead them to select Choice D (9) or cause confusion that leads to guessing.

The Bottom Line:

This problem tests whether students can systematically apply substitution and carefully read what the question asks for. The mathematics is straightforward, but attention to detail in both calculation and question interpretation is crucial.